Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation

We show that a set of gates that consists of all one-bit quantum gates (U(2)) and the two-bit exclusive-or gate (that maps Boolean values \((x,y)\) to \((x,x \oplus y)\)) is universal in the sense that all unitary operations on arbitrarily many bits \(n\) (U(\(2^n\))) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized Deutsch-Toffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two-and three-bit quantum gates, the asymptotic number required for \(n\)-bit Deutsch-Toffoli gates, and make some observations about the number required for arbitrary \(n\)-bit unitary operations.

Cryogenic detectors are extremely sensitive and have a wide variety of applications (particularly in astronomy), but are difficult to integrate into large arrays like a modern CCD (charge-coupled device) camera. As current detectors of the cosmic microwave background (CMB) already have sensitivities comparable to the noise arising from the random arrival of CMB photons, the further gains in sensitivity needed to probe the very early Universe will have to arise from large arrays. A similar situation is encountered at other wavelengths. Single-pixel X-ray detectors now have a resolving power of DeltaE < 5 eV for single 6-keV photons, and future X-ray astronomy missions anticipate the need for 1,000-pixel arrays. Here we report the demonstration of a superconducting detector that is easily fabricated and can readily be incorporated into such an array. Its sensitivity is already within an order of magnitude of that needed for CMB observations, and its energy resolution is similarly close to the targets required for future X-ray astronomy missions.